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ANIMAL GENETICS |
CSIRO Livestock Industries, Queensland Bioscience Precinct, St. Lucia, Queensland 4067, Australia
Abstract
We proposed a novel statistical approach for the analysis of cDNA experiments based on mixed-model methodology combined with mixtures of distributions. Our objective was to detect genes that may be involved in conferring heritable differences in susceptibility to common infections in intensive pig production. We employed a microarray expression profiling strategy and a mixed-model approach to the analysis of the expression data. A cDNA microarray of pig with 6,420 probes from immune tissues and cells was used to compare gene expression in peripheral blood leukocytes of two pigs showing extreme performance in their response to infection with Actinobacillus pleuropneumoniae. Principal components analyses were used to identify the two most extreme-performing pigs after infection (i.e., pigs whose measured responses to infection fell at the extremes). Blood samples and expression profiles from 0 to 24 h after infection were compared using a bivariate, mixed-model approach, in which the effect gene x immunological status interaction was treated as a random effect. Bayesian model-based clustering via mixtures of normal distributions of the resulting BLUP of the random interaction was approached and resulted in a list of 307 differentially expressed genes, of which 179 were down-regulated in the susceptible pig. The majority of the differentially expressed genes were derived from a cDNA library of leukocytes of A. pleuropneumoniae-challenged pigs that were subtracted against leukocytes before the challenge. These results provide evidence that the proposed statistical approach was useful in enhancing the knowledge of the mechanisms involved in the genetics of the immune response.
Key Words: Complementary DNA Gene Expression Microarray Swine
Introduction
Gene expression microarray technology can expedite the identification of genes responsible for infectious disease pathogenesis in livestock as well as an elucidation of their mechanisms (Kato-Maeda et al., 2001
). Actinobacillus pleuropneumoniae, the etiologic agent of contagious pleuropneumonia in pigs, has a great impact on the pig industry worldwide. In Australia, the chronic form of the disease has been estimated to cost $64 per sow and year (Blackall, 2001
). These economic losses relate to the poor performance of infected pigs expressed as decreased weight gain and low feed efficiency or increased death rate (Taylor, 1999
; Hoflack et al., 2001
).
One challenge presented by the large data sets from microarray experiments is the development of accurate data processing and analysis techniques pointing towards the reliable detection of transcripts differentially expressed as a result of treatment effects. New statistical methods for the analysis of microarray data are being proposed in the literature at an incredible pace. A recent review of statistical tests for differentially expressed genes in microarray experiments can be found in Cui and Churchill (2003)
. The authors identify the mixed-model ANOVA method as a general and powerful approach for microarray experiments with multiple factors and several sources of variation.
The objective of this article is to present a mixed-model approach for the analysis of cDNA microarray gene expression data from pigs following bacterial challenge. The resulting BLUP for the gene expression x immunological status interaction were processed through model-based clustering via mixtures of normal distributions to identify differentially expressed genes. The approach was tested on RNA from the peripheral blood leukocytes from two extreme-performing pigs in terms of susceptibility to pleuropneumonia at 0 and 24 h postchallenge with A. pleuropneumoniae.
Materials and Methods
Animals, Bacterial Challenge, Selection Criteria, and RNA Extraction
An animal ethics committee approved all animal procedures. Eighteen 28-wk-old male pigs (predominantly Large white x Landrace) free of A. pleuropneumoniae and weighing on average 33 ± 5 kg were housed in individual pens in two climate-controlled separate air spaces with two rooms per air space. These animals were part of a larger experiment conducted at the Livestock Industries division of the Commonwealth Scientific and Industrial Research Organization (CSIRO) of Australia. Briefly, pigs were fed a commercial diet in individual feed troughs containing 10 g lysine/kg and 13.5 MJ digestible energy/kg (DM basis) at 0900 each day with the residual food removed for the calculation of daily feed intake.
Pigs were acclimatized to these environmentally controlled rooms for 8 d before challenge. Then pigs were fitted with venous catheters 1 d before the challenge. At challenge, pigs were given 1 x 105 cfu of A. pleuropneumoniae (serotype 1, HS54) endotracheally. In addition to monitoring clinical signs like coughing, lethargy, anorexia and labored breathing, a blood sample (15 mL) was collected from each pig immediately before infection (T0) and 24 h after infection (T24) into tubes containing 150 µL of 15% EDTA. The blood was centrifuged (453 x g for 15 min at 4°C) and stored at 20°C following removal of 2 mL of plasma. After 8 d, all pigs were weighed, killed, and necropsied to determine the type and extent of lung pathology.
To identify the two most extreme-performing individuals among the 18 infected pigs, a combination of seven key performance measurements was used, including: 1) percentage of weight gain (WTP); 2) calcitonin-receptor expression level (CTR); 3) percentage of lung score damage (LSP); 4) total clinical score (TCS); 5) feed intake on d 2 (FI2); 6) feed intake on d 5 (FI5); and 7) feed intake on d 7 (FI7) after the challenge. The PRINCOMP procedure of SAS (Version 8.2; SAS Inst. Inc., Cary, NC) was used to perform principal components analysis of the seven performance measurements. The most extreme pigs were labeled as resistant (RES) and susceptible (SUS). Blood samples, taken at time 0 and at 24 h after infection, from these extreme-performing pigs, were used for subsequent microarray experimentation.
Leukocyte RNA was extracted from frozen blood samples and DNAse treated using the Qiagen RNeasy kit (Qiagen, Hilden, Germany), using the manufacturers instructions. Muscle RNA was extracted from porcine skeletal muscle using TRIzol (Invitrogen, Carlsbad, CA) and DNAse treated. Amplified RNA was prepared using Ambions aRNA kit (Ambion, Austin, TX), following manufacturers instructions.
Microarray Design
The main objective of the gene expression experiment was to develop a focused microarray platform to identify which genes were differentially expressed between the RES and the SUS animals over the 24-h trial period. The array contained 7,776 elements (subsequently referred to as simply genes) comprising 6,420 anonymous cDNA clones obtained from 10 subtracted libraries using the PCR-Select cDNA subtraction kit (Clontech, Palo Alto, CA), 68 cDNA clones of known function, and six scorecard controls (Amersham Bioscience, Piscataway, NJ) including elements from other print-facility users. The tissues that were explored for the generation of the subtracted libraries were from spleen, liver, lymph node, lymphocytes, leukocytes, and muscle. The prepared cDNA fragments were arrayed in single spots in duplicated grids at the Institute of Molecular Bioscience (University of Queensland, Brisbane, Australia) on glass slides (Eppendorf, Hamburg, Germany) using a Virtek Microarrayer with the Stealth 48 Pin head and Micro Spotting Pins (Telechem International Inc., Sunnyvale, CA) at a spacing of 220 µm. Each array contained 15,552 spots arranged in 48 blocks of 18 rows x 18 columns.
For the microarray experiments, a control reference design was developed. The availability of reference vs. treatment RNA as well as the cost of the arrays themselves was taken into consideration for the development of the design. In a reference design, an extraneous reference sample is (usually) used along with the RNA of interest. Every sample of interest is compared with this sample in a hybridization. The design is intuitive: every RNA of interest can be compared indirectly because each is compared directly to the reference. Kerr and Churchill (2001b)
provide details of and alternatives to the reference design in microarray experiments.
Two control reference samples were chosen using total RNA or amplified RNA from either pure leukocytes (Lk) or a 1:2 mixture of muscle tissue and leukocytes (MLk). Reference RNA samples were labeled with fluorescent green dye (G), using direct incorporation of Cye3-dUTP during the Superscript II reverse-transcribed cDNA synthesis step (Invitrogen, Carlsbad, CA). For each combination of animal (RES and SUS) and time (T0 and T24) two aRNA samples (i.e., technical replicates) were directly labeled with fluorescent red dye (R) using direct incorporation of Cye5-dUTP. In total, 16 cDNA microarray slides were used in this study.
The GenePix 4000 optical scanner and the image analysis software GenePixPro 3.0, both from Axon Instruments Inc. (Union City, CA), were used to quantify the expression intensities. This software provides a distinct quality reading for bad-quality spots, which were subsequently excluded from the analyses. Also, only genes that scored twice within each microarray slide were used in this study. Finally, the accuracy of the resulting R and G signals was assessed from the correlation between the mean and median signal intensities and estimated by dividing the smaller of the mean or median by the larger for both fluorescent channels in a spot (Tran et al., 2002
). These editing criteria resulted in 414,936 intensity readings (half R and half G, and each with a foreground and a background component) across the 16 microarray slides and from 6,456 genes out of the original 7,776. For these readings, the R and G intensity levels were background-corrected by subtracting the background (Rb and Gb) from the foreground (Rf and Gf) intensities. Thus, for analyses, R = Rf Rb and G = Gf Gb.
Measurement of Differential Gene Expression
A base-2 logarithmic (log2) transformation was applied to the background-corrected intensity levels R and G so that they approximated a normal distribution. In order to reduce the influence of within-slide spot variation without estimating it, the average of the two readings for each gene in each array slide was used as a measure of Mi as follows:
![]() | [1] |
where Ri1 andGi1 are the red and green intensity readings, respectively, for gene i from spot 1, and similarly for Ri2 and Gi2 from spot 2.
Location normalization was applied to the ratio values in Mi from Eq. [1
] by subtracting the within-slide median. The median was used because it is more robust against outliers than the mean. This within-slide location standardization assumes that most genes, at least a half, will not be differentially expressed. It further assumes that, within each microarray, changes are roughly symmetric around the median and across all intensities.
For each animal (RES and SUS) and reference design (Lk and MLk), a measure of possible differential gene expression from T0 to T24 was obtained by subtracting the median-corrected M ratio values at T0 from those at T24. Two variables, one for each animal type, were computed for each gene and sample combination as follows:
![]() | [2] |
![]() | [3] |
In this notation, subscript i refers to gene (i = 1 to 6,456), j refers to control reference design (j = 1 and 2 for Lk and MLk, respectively), k refers to sample 1 or 2 evaluated at T24, and m refers to sample 1 or 2 evaluated at T0. A positive (or negative) value in RESijkm indicates an increase (or decrease) in the expression of gene i from T0 to T24 in the resistant animal. Similarly, a positive (negative) value in SUSijkm indicates an increase (decrease) in the expression of gene i from T0 to T24 in the susceptible animal.
Mixed-Model Equations and Estimation of (Co)Variance Components
The mixed-model for the bivariate analysis of observations in Eq. [2
] and [3
] can be written as
![]() | [4] |
where
In total, there were 49,366 observations of which 44,136 corresponded to observations on gene expression change in both yR and yS, 2,596 corresponded to observations on gene expression change in only yR, and 2,634 corresponded to observations on gene expression change in only yS.
There were 136 levels for comparison group fixed effects, defined by those gene expressions corresponding to genes from the same plate library (with 17 levels), the same control reference design (with two levels) and the same sample contrast in the T0-with-T24 comparison (two technical replicates by two time points). The 17 levels of plate library originated from 10 subtracted libraries of anonymous cDNA clones, plus the set of 68 cDNA clones of known function, plus the six scorecard controls.
For the model in Eq. [4
], the (co)variance matrix for the random effects was assumed to be as follows
![]() | [5] |
where
2gR (
2gS)
gRgS
2eR (
2eS)
eReS
Writing out the equations for each variable in the model separately, the mixed-model equations become
![]() | [6] |
where Gij (Eij) are elements of G1 (E1). The total number of equations represented in Eq. [6
] is 13,184 coming from twice 136 comparison group fixed effects plus twice 6,456 gene random effects.
Estimates of (co)variance components and solutions to the mixed-model equations were obtained by Method
(Reverter et al., 1994
) using an acceleration method described by Druet et al. (2001)
. The multiplicative iterative algorithm to update (co)variances for traits i and j was
![]() | [7] |
where
i and
j represent vectors of estimated solutions from the complete data set, and
ip and
jp represent vectors of estimated solution from a 50% random partial data. At convergence, the G matrix is symmetric, and during iteration symmetry was forced by averaging the off-diagonal elements.
Data from each animal were analyzed 25 times with different 50% partial data subsets selected randomly to obtain BLUP in
ip and
jp. The convergence criterion was ri = 1.0 ± 0.0001, where ri is the regression for variance component i. Sampling standard errors of the estimates were calculated from the SD of 25 estimates from different subsamples. The ABTK2.0, Animal Breeders ToolKit, software (Golden et al., 1992
) was used both for the estimates of variance components and for the solutions to the mixed-model equations.
Bayesian Model-Based Clustering
Solutions to the mixed-model equations are BLUP of gene effects
R and
S for RES and SUS, respectively. For each gene in i, the difference
![]() | [8] |
provides a measure to be investigated in order to identify differentially expressed genes in RES relative to SUS. Large positive di values are likely to belong to genes whose expression is up-regulated in the RES animal and down-regulated in the SUS animal during the 24-h postinfection period. Similarly, large negative di values are likely to belong to down- (or up-)regulated genes in the RES (or SUS) animal in the same period.
Bayesian model-based clustering with a known number of components was approached to isolate differentially expressed genes with di values assumed to be independent observations from a mixture density with k (possible unknown but finite) components and with probability density function:
![]() | [9] |
where
(d; µj, Vj) denotes the normal density function with mean µj and covariance matrix Vj, and the mixing proportions
j are constrained to be nonnegative and sum to unity. All unknown parameters are represented in
k for a k-component (or k-cluster) mixture model. In the present study, mixture models with up to five components (or clusters) were contemplated.
Following Raftery (1996)
the following prior densities were used:
![]() | [10] |
where
(a, b) denotes a gamma density with mean a/b and variance a/b2; N(a, b) denotes a normal distribution with mean a and variance b;
= (
1, ...,
k); and Dir(
1,...,
k) denotes the Dirichlet distribution with parameter
.
Following Richardson and Green (1997)
, prior hyperparameters were chosen to be data-dependent-constant so that the prior distribution was relatively flat over the range of values that could be expected. Finally, the Gibbs sampler proceeded by sampling successively from the following conditional distributions:
![]() |
where the latent data u = (u1, ..., un) are indicative of the mixture component from which di were generated. The Gibbs sampler was run until a Markov chain of length 12,000 was generated, the first 2,000 (burn-in) were discarded, and averages from the remaining 10,000 samples were used to obtain point estimates for parameters in Eq. [9
].
Up to five components (clusters) were explored for the model in Eq. [9
]. Criteria for model selection include a combination of the likelihood evaluation (logL) as well as the Akaike information criterion (Akaike, 1969
) and the Bayesian information criterion (Schwartz, 1978
).
Once the mixture model of choice has been identified, the probability of each data point belonging to each cluster was given by the posterior probability in
![]() | [11] |
Further, a data point in di (and thus the ith gene) was classified to a given cluster if its posterior probability was the largest.
Software Availability
Software named BAYESMIX was developed using FORTRAN90 to perform Bayesian model-based clustering via mixtures of normal distributions and is available from the corresponding author on request and for noncommercial use only. Further details of the software are given in Reverter et al. (2003b)
.
Results
Table 1
provides summary statistics of key performance traits and principal components analysis results for the 18 infected pigs involved in this study. The first principal component explained 53% of the total variation and had a clear biological interpretation with positive weights for favorable traits (weight gain and feed intakes) and negative weights for unfavorable (i.e., clinical) traits. Therefore, this first principal component was used to rank individuals in terms of susceptibility to Actinobacillus pleuropneumoniae.
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Table 3
presents the number of observations and least square means for each level of reference sample and plate of origin as obtained using the GLM procedures of SAS (SAS Inst. Inc., Cary, NC). The 46,732 observations in yR averaged 0.129 and ranged from 4.033 to 5.017 with a SD of 0.843. The 46,770 observations in yS averaged 0.028 and ranged from 4.791 to 7.633 with a SD of 1.008.
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estimates of (co)variance components. The number of iterations to achieve convergence averaged 31 and ranged from 28 to 45. In this situation, with few levels of fixed effects relative to the large amount of observations in each, and assuming an identity matrix to describe dispersion in random gene expression effects, Method
was found to be particularly stable (judged by sampling variation, Table 4
|
Mean, SD, minimum and maximum values for resulting BLUP differences in di from Eq. [8
] were 0.000, 0.793, 5.214 and 3.378, respectively. Fitting of mixtures of normal distributions to the quantities in di revealed the following three-component (or cluster) model as the one of choice:
![]() |
The majority of records fell into the middle cluster with zero mean and intermediate variance and corresponded to genes not differentially expressed between the RES and the SUS animals. The first cluster corresponded to genes whose expression from T0 to T24 was decreased in the RES and increased in the SUS. There were 128 genes classified into this first cluster. The majority of these genes originated from the lymph node vs. liver tissue subtractive library. These 128 genes presented a di value that was
1.851 (or 2.33 SD). The last cluster corresponded to 179 genes whose expression from T0 to T24 was increased in the RES and decreased in the SUS. The majority of these candidates resulted from the RNA of leukocytes of A. pleuropneumoniaechallenged pigs, where the leukocytes 24 h postchallenge were subtracted against leukocytes before the challenge. The di observed for these 179 differentially expressed genes was
1.626 (or 2.05 SD). Figure 2
illustrates the scatter plot of
S vs.
R for the 6,456 genes and where the ones identified as differentially expressed are highlighted. Note the presence of 11 genes classified into Cluster 1 although their expression was up-regulated in both RES and SUS pigs. Similarly, there were eight genes classified into Cluster 3 even though their expression was down-regulated in both pigs RES and SUS.
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Current management of A. pleuropneumoniae infections includes vaccination and use of antimicrobial growth promotants. However, these measures only slightly confine the commercial consequences of the pathogen. Although the continuous use of antibiotics is expensive and cannot prevent the establishment of A. pleuropneumoniae in the lungs, it is also speculated to increase the emergence of antibiotic resistance. Vaccination has only a marginally protective effect because several serotypes are prevalent in various countries and even vaccinated pigs can remain carriers of the pathogen in a subclinical or chronic state (Wongnarkpet et al., 1999
; Chiers et al., 2002
). By learning more about the pig immune system and modulating its responses, antibiotics and chemicals currently used to control disease may be reduced or replaced, with the added benefit of improving health and increasing disease resistance.
In the present study, not all infected pigs showed the same degree of symptomatic response to the A. pleuropneumoniae challenge. This is indicative of what happens during an outbreak in a commercial piggery. Pigs displaying extreme phenotypes measured in terms of performance (either high or low performers) after being challenged with A. pleuropneumoniae are obvious targets for a global functional genomic approach to reveal genes responsible for the degree of susceptibility to infection. In keeping with studies reported elsewhere (Balaji et al., 2002
), pigs used in this experiment displayed anorexia, along with other relevant clinical signs (Table 1
), within a few hours after A. pleuropneumoniae challenge. There is also considerable evidence for enhanced production of mRNA for inflammatory mediators in lung tissue of pigs infected with A. pleuropneumoniae (Baarsch et al., 2000
). Therefore, it was anticipated that measuring changes in gene expression levels in peripheral blood leukocytes at 24 h after the challenge might distinguish genes involved in the pathogenesis of A. pleuropneumoniae pneumonia.
There is currently no consensus about how to best eliminate sources of error in the intensity readings of microarray experiments. Two commonly discussed approaches are normalization adjustment of data before statistical analysis (Yang et al., 2002
) and adjusting for sources of bias and confounding with a linear model (Kerr and Churchill, 2001a
; Wolfinger et al., 2001
). Fitting fixed effects aims at normalizing gene expression data by accounting for systematic sources of variation, such as array, dye, variety, and samples. In a complex experiment in which the RNA samples have a nontrivial experiment design structure, it may be desirable to include both fixed and random terms in the treatment x gene interaction component of the model. Simultaneously solving for fixed and random effects as in the mixed model of Eq. [4
] adjusts for the possibility of different expression intensities of a given gene across levels of comparison group as well as variability both across and within genes. In this situation, the recently reported two-stage approach of Dobbin and Simon (2002)
would be most inadequate as it would ignore fixed by random off-diagonal elements of the information matrix in the left-hand side of Eq. [6
]. Mixed models can admit more general covariance structure and will provide shrinkage of estimated effects that can reduce bias. The optimality of mixed models to assess gene significance from cDNA microarray expression data was previously reported by Wolfinger et al. (2001)
.
The heterogeneity observed at the gene expression level between RES and SUS is not unexpected in microarray gene expression analysis given the wide variety of known gene functions. Gene expression heterogeneity has been documented in other studies, such as Golub et al. (1999)
and Dudoit et al. (2002)
. From a biological viewpoint, the lack of correlation between gR and gS observed in this study is encouraging and indicates that the set of genes responsible for a given change in genetic expression (i.e., either up- or down-regulation) between T0 and T24 in the RES animal is not related to the set of genes responsible for the same type of change in genetic expression in the SUS animal and in the same time period. This indicates that distinct sets of genes may be induced by infection in the resistant and susceptible phenotypes.
Although observations on RES and SUS individuals were not compared directly in the same microarray, but through the same reference sample, an estimate of residual correlation was obtained and attributed to spatial correlation due to proximity on slide array. This positive residual correlation estimated at 0.256 ± 0.009 indicates that the nongenetic factors (i.e., array, block, plate of origin) responsible for an increase in gene expression in RES are also related to those responsible for an increase in SUS and vice versa.
Model-based clustering via mixture of distributions has been identified as a method of choice for identifying which genes have differential expression levels. In livestock species, this technique was recently used to identify differentially expressed genes in bovine muscle tissue in response to varying levels of energy and protein in the diet (Reverter et al., 2003a
). Model-based clustering clearly defines cluster subpopulations with a certain distribution, and clustering results are stable. Several statistical methods can be applied to estimate the number of clusters (Yeung et al., 2001
; Pan et al., 2002b
). In addition, model-based clustering has been shown to provide an elegant framework to calculate the power of detecting a specified magnitude of change (Rekaya, 2002
) as well as to estimate the number of replicates needed for precise inferences (Pan et al., 2002a
). In all the above-mentioned studies, model-based clustering was applied directly to intensity ratios or to linear combinations of intensity ratios (in the form of a t-statistic). A novel approach was described by Allison et al. (2002)
, exploiting, under the null hypothesis, the uniform distribution of P-values on the interval [0, 1] regardless of the statistical test used. The authors then proposed the fitting of a mixture of beta distributions to these P-values to identify the gene comparisons of interest. To the best of our knowledge, the present study is the first report in which fitting a mixture of distributions is applied to the BLUP resulting from the fitting of mixed-model equations. An alternative and possibly preferable option could be to integrate the cluster analysis with the mixed-model analysis as recently described by Gianola et al. (2004)
within the context of inferring susceptibility to mastitis in dairy cattle.
The statistical approach used in our study resulted in a list of differentially expressed genes that originated mostly from two distinct subtracted cDNA libraries (Table 5
) adding biological meaning to the cluster results from the mixture analysis. For instance, 109 out of the 128 differentially expressed genes downregulated in RES and upregulated in SUS are part of a lymph node vs. liver cDNA library and 18.6% of clones from this library (with 672 clones) were identified as being differentially expressed. In contrast, the majority of differentially expressed genes (91 out of 179) that were up-regulated in RES and downregulated in SUS were derived from an immune cell subtractive library in which pig blood leukocytes 24 h after challenge were subtracted against blood leukocytes before challenge (WBC-F in Table 5
) and 14.6% of clones from the WBC-F library (with 714 clones) were identified as being differentially expressed. Additionally, another high proportion of differentially expressed genes showing this profile (i.e., upregulation in RES and downregulation in SUS) were identified as being part of immune vs. nonimmune tissue cDNA libraries generated by subtracting cDNA of activated lymphocytes with muscle tissue cDNA and vice versa (in Table 5
, PLMU-F and PLMU-R).
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We are confident that the experimental approach and analytical methods presented here are likely to result in biologically relevant data. However, the fact that only the two most extreme-performing pigs (one RES and one SUS) were included in this analysis implies that caution must be taken when interpreting the results. Some of the differentially expressed genes identified in this work could be responses to things affecting the pigs life other than infection. Our intention is to direct further research to a new microarray experiment incorporating additional biological replicates and a superior design. This extended analysis will be followed by nucleotide sequencing of differentially expressed genes and the development of independent tests to confirm the expression patterns characterized by the microarray study.
Implications
The present study explores gene expression in peripheral blood leukocytes of two pigs showing extreme performance in their response to infection with Actinobacillus pleuropneumoniae. The statistical approach to identify differentially expressed genes is based on mixed-model methodology to analyze the gene expression levels combined with Bayesian model-based clustering of the solutions for the gene x immunological status interaction. The resulting list of differentially expressed elements is biased toward immune-relevant genes and seems to reflect the contrasting effect of the disease challenge and the appearance of the extreme pig phenotypes in the trial.
Footnotes
1 The authors acknowledge the Australian Pork Limited for financial support. The assistance of C. Dimmock also is gratefully acknowledged. ![]()
2 Correspondence: 306 Carmody Road (phone: +61-7-3214-2392; fax: +61-7-3214-2881; e-mail: tony.reverter-gomez{at}csiro.au).
Received for publication June 17, 2003. Accepted for publication January 27, 2004.
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